adult lactose tolerance entered the human population (they now think) through one tribe in northern Europe and four tribes in Africa (based on only five genetic ways it has occurred and their distribution), so it is not actually "normal" to be lactose tolerant (I think this is why Every Household In America had Pepto-Bismol in the medicine cabinet for so many years!). In my family, the girls get it 100% when we hit puberty, but I know I had it before that because I definitely grew up wondering why everyone freaked out if they got diarrhea because I had it like All The Time and it was clearly just not that big a deal for me (I'm sure it probably stunted my growth or some nutritional thing, but really, I was a Fine Kid in general).
That said, I missed a lot of school when I tried to be "good" in 8th grade and eat a breakfast with a serving of milk every morning--Xtreeeeeme Nausea, oy ...
At my worst (about age 22 when I figured it out), eating one Hershey's Kiss would make me nauseated. My sister got rejected from the Army, no kidding, because her lactose intolerance was too severe ... despite an appeal by her recruiter to the Surgeon general of the Army(!!!) because she was such a strong candidate otherwise and wanted to go into the intelligence wing (not so much the standard-rations problem). Dude!
Anyhow, if your daughter's not allergic (which from the advice you are getting I am sure you will check out ;) ), and if she has only got a low-tolerance (like me as a kid) and not an INtolerance (like me now), after you cut the dairy for a while she should be able to eat low-lactose dairy, maybe every other day (so the limited enzymes can build up enough to do their job)--like natural yogurts (not conventional ones, which often have lactose added BACK IN to sweeten them up) and hard cheeses and butter and cultured sour cream and cultured buttermilk (those last two are often chemically created instead of cultured, and the lactose is not then eaten up by the bacteria).
There are lactose-removed milks now (we use Organic Valley) ... after you remove dairy for a few days, try one of those. I've heard goat milk is also lactose-low.
As she gets older, if lactose intolerance is a concern, watch multivitamins, some pills use lactose as a filler (another "responsible" thing I did to myself in jr. high and high school, every morning until I read the ingredients). Also, any stress that negatively affects my overall health will also lower my tolerance--sometimes when I am not stressed I can eat soft cheese, sometimes when I'm stressed I avoid parmesean ...